Hausch, Ziemba & Rubinstein (1981) developed a betting system (the Dr. Z system) that empirically demonstrated positive profits in two racetracks. The Dr. Z system assumes running times are distributed exponentially but the use of other distributions for running times (Henery (1981) and Stern (1990)) produces a better fit in some racetracks although the better fit is at the cost of severely increased complexity in computing ordering probabilities. Lo & Bacon-Shone (1992) proposed a simple model of computing ordering probabilities which is a good approximation to those based on the Henery model and the Stern model. In this paper. we add this model to the Dr. Z system and use a simple way of computing ordering probabilities which is a good approximation to those based on the Henery model. With data sets in the U.S. and Hong Kong, we show improved profit over the Dr. Z system at lower levels of risk. With the special return formula in Japan. our model does not have a big difference in profits from the Dr. Z system.

Hausch, Ziemba & Rubinstein (1981) developed a betting system (the Dr. Z system) that empirically demonstrated positive profits in two racetracks. The Dr. Z system assumes running times are distributed exponentially but the use of other distributions for running times (Henery (1981) and Stern (1990)) produces a better fit in some racetracks although the better fit is at the cost of severely increased complexity in computing ordering probabilities. Lo & Bacon-Shone (1992) proposed a simple model of computing ordering probabilities which is a good approximation to those based on the Henery model and the Stern model. In this paper. we add this model to the Dr. Z system and use a simple way of computing ordering probabilities which is a good approximation to those based on the Henery model. With data sets in the U.S. and Hong Kong, we show improved profit over the Dr. Z system at lower levels of risk. With the special return formula in Japan. our model does not have a big difference in profits from the Dr. Z system.